(1) Land complexity index (*LCI*) [34,39]:

The complexity of land-use systems mainly reflects the external pressures associated with human activities and land development intensity. For the measurement of external pressure, it is mainly considered from the perspective of the comprehensive influence of the space unit and its surrounding area. Fractals are an effective tool for describing the spatial pattern of nature and the spatial complexity of geographical phenomena. Therefore, the area-weighted mean patch fractal dimension (*AWMPFD*) was used as a spatial index to describe the complexity of land use patches, with a view to reflecting the influence of land-use processes in neighborhoods on current land-use types. In general, the fractal values of natural landscapes that are less disturbed by human activities are high, while the fractal values of man-made landscapes that are highly influenced by human activities are low [40]. The calculation method was as follows (Formula (2)):

$$LCI = AWMPFD = \sum\_{i=1}^{m} \sum\_{j=1}^{n} \frac{2 \ln(0.25 P\_{ij})}{\ln a\_{ij}} \times \frac{a\_{ij}}{A} \tag{2}$$

In this formula, *Pij* refers to the perimeter of the *j*th landscape patch of space type *i*; *aij* refers to the area of the *j*th landscape patch of space type *i*; *A* refers to the total area of the spatial unit; *m* refers to the number of space types; and *n* refers to the number of landscape patches. To simplify and standardize the calculations, the obtained index values were standardized to 0~1.

#### (2) Land fragility index (*LFI*) [39,41]:

The *LFI* represents the resistance of landscape patches to external pressures. The role of different landscape types in maintaining biodiversity, and improving overall structure and function varies. This difference is related to the stages in which different landscapes are in the natural succession process. In general, ecosystems in the primary succession stage, with simpler food chain structure and lower biodiversity are more fragile [42]. The fragility

of each landscape in the space was used to calculate the *LFI*. The calculation method was as follows (Formula (3)):

$$LFI = \sum\_{i=1}^{m} \sum\_{s=1}^{r} fis \times \frac{ais}{A} \tag{3}$$

In this formula, *fis* refers to the landscape fragility of land use types in space type *i*; *ais* refers to the landscape patch area of land-use types in space type *i*; *A* refers to the total area of the spatial unit; *m* refers to the number of space types; and *r* refers to the number of land-use types.

Land-use types were assigned landscape fragility values [31,43], as shown in Table 1. To simplify and standardize the calculations, the obtained index values were standardized to 0~1.


**Table 1.** Assessment of the landscape fragility of agricultural spaces and ecological spaces in Lin'an District.
